Servers and bandwidth aren't free. Someone needs to pay for it. There are roughly seven ways to fund a website:

• Complete volunteering, and maintainer pays all fees out of pocket. Only makes sense for very small projects, or when the maintainer is rich and has a great deal of passion or otherwise self-interest in the project.
• Strictly fund the website with donations. That's more or less how Wikipedia works. It can be hard to make ends meet, and it typically only works if your website basically offers community service like a charity or if you have very passionate users.
• Freemium model: most users are just leeches and are subsidized by the few who pay for the premium version. This is more or less how free-to-play video games work, and some newspapers survive this way. It can be difficult to convince people.
• Members only: you literally cannot use the website unless you pay. A lot of SAAS websites, especially for businesses, work this way. It can be a hard sell for a lot of service categories.
• Ads. Sometimes combined with a freemium model, where you can pay to remove the ads. YouTube works this way.
• Sell user data to advertisers or more sinister entities. Only possible if you have valuable user data to sell. Most social networks get a significant portion of their revenue from this method, but they typically combine it with ads.
• Use venture capital to disturb an existing market at a loss, get massive mindshare and maybe even kill existing competition, and jack the prices up to repay your debts and turn a profit once you have customers and the market is more favourable. Airbnb works this way.

What would you do for review sites? News sites? Video game wikis?

Wouldn't it suck if a wiki for an old game was just gone because there aren't many players anymore, and now you just can't access the info in it?

I've got a feeling that advertising companies have ways to differentiate real and fake clicks. Best case scenario, they wouldn't count those. Worst case scenario, they could notice that too many clicks are fake and revoke the monetization for a website.

If captchas exist, surely they can use similar methods to catch ad cheats like that.

This is older, and not quite the same but back when I was into private Ragnarok Online servers, it was pretty well-known among server admins that you couldn't ask people to click your ads. Either because you asked, either because they noticed unusual activity, Google would demonetize the ads pretty quickly.